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Particle moving in a one-dimensional potential

  1. Mar 17, 2012 #1
    1. The problem statement, all variables and given/known data

    A particle moving in a one-dimensional potential is in a state such that its wavefunction at time t=0 is:

    Psi(x,0)=A(x-a)x, 0<=x<=a, and
    Psi(x,0)=0, otherwise.

    Sketch |Psi(x,0)|^2, which gives the probability distribution describing the position of the particle at time t=0.

    2. Relevant equations

    As above

    3. The attempt at a solution

    I am thrown by Psi in this question. It doesn't even resemble a wavefunction. Am I simply supposed to square the absolute value of the polynomial?
     
  2. jcsd
  3. Mar 17, 2012 #2

    vela

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    Yes. Why do you say it "doesn't even resemble a wavefunction"?
     
  4. Mar 17, 2012 #3
    Because its not a periodic function.
     
  5. Mar 17, 2012 #4
    I'm obviously overlooking something important here. Please help.
     
  6. Mar 17, 2012 #5

    HallsofIvy

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    Why should it be periodic? Are sure what is meant by a "waveform" here?
     
  7. Mar 17, 2012 #6
    Shouldn't a wavefunction resemble a wave? ie be periodic?
     
  8. Mar 17, 2012 #7
    You are confusing a wavefunction with a periodic function such as a sinusoid of varying harmoics, etc. The wavefunction is essentially a probability amplitude for (in this case) the location of a particle.

    It is, (in this case) a one dimensional wave and you can model its motion using a (rather famous) relation that looks quite close to the wave equation, shown here:

    [ tex ] \nabla^2 f(x,y,z) = \frac{1}{c^2} \frac{\partial f(x,y,z)}{\partial t} [ /tex ]
     
    Last edited: Mar 17, 2012
  9. Mar 17, 2012 #8

    vela

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    Nope. A pulse traveling down a string, for instance, is a wave. There's no requirement for periodicity at all.
     
  10. Mar 18, 2012 #9
    by the way....why isn't my tex being formatted?
     
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